Law of cosines

From Math Images

The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of a
particular angle.

When to use it: SAS, SSS.

Proof

Let be oriented so that is at the origin, and is at the point.

Distance Formula

is the distance from to .

Substituting the appropriate points into the distance formula gives us